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Journal articles on the topic 'Proximal operator'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Li, Jia, Cong Fang, and Zhouchen Lin. "Lifted Proximal Operator Machines." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 4181–88. http://dx.doi.org/10.1609/aaai.v33i01.33014181.

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We propose a new optimization method for training feedforward neural networks. By rewriting the activation function as an equivalent proximal operator, we approximate a feedforward neural network by adding the proximal operators to the objective function as penalties, hence we call the lifted proximal operator machine (LPOM). LPOM is block multiconvex in all layer-wise weights and activations. This allows us to use block coordinate descent to update the layer-wise weights and activations. Most notably, we only use the mapping of the activation function itself, rather than its derivative, thus

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2

Yang, Yixuan, Yuchao Tang, and Chuanxi Zhu. "Iterative Methods for Computing the Resolvent of Composed Operators in Hilbert Spaces." Mathematics 7, no. 2 (2019): 131. http://dx.doi.org/10.3390/math7020131.

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The resolvent is a fundamental concept in studying various operator splitting algorithms. In this paper, we investigate the problem of computing the resolvent of compositions of operators with bounded linear operators. First, we discuss several explicit solutions of this resolvent operator by taking into account additional constraints on the linear operator. Second, we propose a fixed point approach for computing this resolvent operator in a general case. Based on the Krasnoselskii–Mann algorithm for finding fixed points of non-expansive operators, we prove the strong convergence of the sequen

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3

KHATIBZADEH, HADI, and SAJAD RANJBAR. "MONOTONE OPERATORS AND THE PROXIMAL POINT ALGORITHM IN COMPLETE CAT(0) METRIC SPACES." Journal of the Australian Mathematical Society 103, no. 1 (2016): 70–90. http://dx.doi.org/10.1017/s1446788716000446.

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In this paper, we generalize monotone operators, their resolvents and the proximal point algorithm to complete CAT(0) spaces. We study some properties of monotone operators and their resolvents. We show that the sequence generated by the inexact proximal point algorithm $\unicode[STIX]{x1D6E5}$-converges to a zero of the monotone operator in complete CAT(0) spaces. A strong convergence (convergence in metric) result is also presented. Finally, we consider two important special cases of monotone operators and we prove that they satisfy the range condition (see Section 4 for the definition), whi

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4

INUWA, ADAMU YUSUF, PARIN CHAIPUNYA, POOM KUMAM, and SANI SALISU. "Equilibrium problems and proximal algorithm using tangent space products." Carpathian Journal of Mathematics 40, no. 1 (2023): 65–76. http://dx.doi.org/10.37193/cjm.2024.01.06.

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This paper presents equilibrium problems and their regularized problems in the framework of Hadamard spaces. Using the concept of tangent space products, we introduce a resolvent operator and deduce essential properties in relation to equilibrium problem. Furthermore, we analyze the regularized problems involving resolvent operators. Finally, we establish two convergence results concerning proximal algorithms

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5

Rahaman, Mijanur, Rais Ahmad, Mohd Dilshad та Iqbal Ahmad. "RELAXED Η-PROXIMAL OPERATOR FOR SOLVING A VARIATIONAL-LIKE INCLUSION PROBLEM". Mathematical Modelling and Analysis 20, № 6 (2015): 819–35. http://dx.doi.org/10.3846/13926292.2015.1117026.

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In this paper, we introduce a new resolvent operator and we call it relaxed η-proximal operator. We demonstrate some of the properties of relaxed η- proximal operator. By applying this concept, we consider and study a variational -like inclusion problem with a nonconvex functional. Based on relaxed η-proximal operator, we define an iterative algorithm to approximate the solutions of a variational-like inclusion problem and the convergence of the iterative sequences generated by the algorithm is also discussed. Our results can be treated as refinement of many previously known results. An exampl

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6

Ahmad, Rais, Arvind Kumar Rajpoot, Imran Ali, and Ching-Feng Wen. "Yosida Complementarity Problem with Yosida Variational Inequality Problem and Yosida Proximal Operator Equation Involving XOR-Operation." Journal of Mathematics 2021 (November 27, 2021): 1–15. http://dx.doi.org/10.1155/2021/9362630.

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Due to the importance of Yosida approximation operator, we generalized the variational inequality problem and its equivalent problems by using Yosida approximation operator. The aim of this work is to introduce and study a Yosida complementarity problem, a Yosida variational inequality problem, and a Yosida proximal operator equation involving XOR-operation. We prove an existence result together with convergence analysis for Yosida proximal operator equation involving XOR-operation. For this purpose, we establish an algorithm based on fixed point formulation. Our approach is based on a proxima

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7

Rouhani, Behzad Djafari, and Vahid Mohebbi. "Strong Convergence Theorems for Resolvents of Accretive Operators with Possible Unbounded Errors." WSEAS TRANSACTIONS ON MATHEMATICS 23 (December 31, 2024): 1086–93. https://doi.org/10.37394/23206.2024.23.109.

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In this paper, we study the convergence analysis of the sequence generated by an inexact proximal point method with unbounded errors to find zeros of m-accretive operators in Banach spaces. We prove the zero set of the operator is nonempty if and only if the generated sequence is bounded. In this case, we show that the generated sequence converges strongly to a zero of the operator. This process defines a sunny nonexpansive retraction from the Banach space onto the zero set of the operator. We present also some applications and numerical experiments for our results.

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8

Farajzadeh, A. P., S. Plubtieng, and K. Ungchittrakool. "On Best Proximity Point Theorems without Ordering." Abstract and Applied Analysis 2014 (2014): 1–5. http://dx.doi.org/10.1155/2014/130439.

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Recently, Basha (2013) addressed a problem that amalgamates approximation and optimization in the setting of a partially ordered set that is endowed with a metric. He assumed that ifAandBare nonvoid subsets of a partially ordered set that is equipped with a metric andSis a non-self-mapping fromAtoB, then the mappingShas an optimal approximate solution, called a best proximity point of the mappingS, to the operator equationSx=x, whenSis a continuous, proximally monotone, ordered proximal contraction. In this note, we are going to obtain his results by omitting ordering, proximal monotonicity, a

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9

Moudafi, Abdellatif. "A remark on recent results for finding zeroes of accretive operators." Journal of Applied Mathematics and Stochastic Analysis 2006 (March 23, 2006): 1–6. http://dx.doi.org/10.1155/jamsa/2006/56704.

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By means of the Yosida approximate of an accretive operator, we extended two recent results by Chidume and Chidume and Zegeye (2003) to set-valued operators, and we made the connection with two recent convergence results obtained by Benavides etal for a relaxed version of the so-called proximal point algorithm.

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10

Messina, Carmelo, Salvatore Gitto, Roberta Colombo, et al. "Short-Term Precision and Repeatability of Radiofrequency Echographic Multi Spectrometry (REMS) on Lumbar Spine and Proximal Femur: An In Vivo Study." Journal of Imaging 9, no. 6 (2023): 118. http://dx.doi.org/10.3390/jimaging9060118.

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To determine the short-term intra-operator precision and inter-operator repeatability of radiofrequency echographic multi-spectrometry (REMS) at the lumbar spine (LS) and proximal femur (FEM). All patients underwent an ultrasound scan of the LS and FEM. Both precision and repeatability, expressed as root-mean-square coefficient of variation (RMS-CV) and least significant change (LSC) were obtained using data from two consecutive REMS acquisitions by the same operator or two different operators, respectively. The precision was also assessed in the cohort stratified according to BMI classificati

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11

Alwadani, Salihah. "The Composition of Modified Reflection Operators and Their Fixed Point Sets." European Journal of Pure and Applied Mathematics 18, no. 2 (2025): 6031. https://doi.org/10.29020/nybg.ejpam.v18i2.6031.

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The modified reflection operator plays a crucial role in optimization, particularly in algorithms designed to solve constrained optimization problems. By effectively transforming feasible solutions while maintaining their viability within defined constraints, this operator enables smoother navigation through the solution space. It enhances convergence rates and stability in iterative methods, such as projected gradient descent and proximal algorithms. In this paper, we investigate the fixed point sets of the compositions of three modified reflection operators onto linear closed subspaces. We a

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12

Miller, Sarah M., and Wai-Tat Fu. "The Role of Temporal Sequence Learning in Guiding Visual Attention Allocation." Proceedings of the Human Factors and Ergonomics Society Annual Meeting 51, no. 19 (2007): 1368–72. http://dx.doi.org/10.1177/154193120705101920.

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Models of visual attention allocation suggest that monitoring is driven primarily by proximal cues like bandwidth and value. However, these cues might not always be predictive of the meaningful events an operator is asked to monitor. The aim of the current study is to extend visual sampling models by studying whether sampling can be influenced by more distal cues, like detecting patterns in the monitored signal, when proximal cues, like bandwidth, are not predictive of the meaningful events the operator is asked to monitor. Ten participants completed a task based on Senders' (1964) experiment

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13

Lou, Yifei, and Ming Yan. "Fast L1–L2 Minimization via a Proximal Operator." Journal of Scientific Computing 74, no. 2 (2017): 767–85. http://dx.doi.org/10.1007/s10915-017-0463-2.

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14

Liu, Zhiyong. "Proximal Operator Splitting for Multi-Constraint Dictionary Learning." International Journal of Hybrid Information Technology 10, no. 2 (2017): 107–16. http://dx.doi.org/10.14257/ijhit.2017.10.2.11.

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15

Roig-Solvas, Biel, Lee Makowski, and Dana H. Brooks. "A Proximal Operator for Multispectral Phase Retrieval Problems." SIAM Journal on Optimization 29, no. 4 (2019): 2594–607. http://dx.doi.org/10.1137/18m120227x.

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16

HARUNA, LAWAL YUSUF, GODWIN CHIDI UGWUNNADI, and BASHIR ALI. "On the Proximal Point Algorithm of Hybrid-Type in Flat Hadamard Spaces with Applications." Kragujevac Journal of Mathematics 48, no. 6 (2024): 845–57. http://dx.doi.org/10.46793/kgjmat2406.845h.

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In this paper, we introduce a hybrid-type proximal point algorithm for approximating zero of monotone operator in Hadamard-type spaces. We then prove that a sequence generated by the algorithm involving Mann-type iteration converges strongly to a zero of the said operator in the setting of ﬂat Hadamard spaces. To the best of our knowledge, this result presents the ﬁrst hybrid-type proximal point algorithm in the space. The result is applied to convex minimization and ﬁxed point problems.

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17

CHIDUME, CHARLES, GERALDO SOARES De SOUZA, and VICTORIA UKAMAKA NNYABA. "Approximation of zeros of m-accretive mappings, with applications to Hammerstein integral equations." Carpathian Journal of Mathematics 36, no. 1 (2020): 59–69. http://dx.doi.org/10.37193/cjm.2020.01.06.

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"An algorithm for approximating zeros of m-accretive operators is constructed in a uniformly smooth real Banach space. The sequence generated by the algorithm is proved to converge strongly to a zero of an m-accretive operator. In the case of a real Hilbert space, our theorem complements the celebrated proximal point algorithm of Martinet and Rockafellar for approximating zeros of maximal monotone operators. Furthermore, the convergence theorem proved is applied to approximate a solution of a Hammerstein integral equation. Finally, numerical experiments are presented to illustrate the converge

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18

Heydari, Mohammad Taghi, and Sajad Ranjbar. "Halpern-type proximal point algorithm in complete CAT(0) metric spaces." Analele Universitatii "Ovidius" Constanta - Seria Matematica 24, no. 3 (2016): 141–59. http://dx.doi.org/10.1515/auom-2016-0052.

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AbstractFirst, Halpern-type proximal point algorithm is introduced in complete CAT(0) metric spaces. Then, Browder convergence theorem is considered for this algorithm and also we prove that Halpern-type proximal point algorithm converges strongly to a zero of the operator.

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19

Ertel, Andrew, Jeffrey Nadelson, Adhir R. Shroff, Ranya Sweis, Dean Ferrera, and Mladen I. Vidovich. "Radiation Dose Reduction during Radial Cardiac Catheterization: Evaluation of a Dedicated Radial Angiography Absorption Shielding Drape." ISRN Cardiology 2012 (September 4, 2012): 1–5. http://dx.doi.org/10.5402/2012/769167.

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Objectives. Radiation scatter protection shield drapes have been designed with the goal of decreasing radiation dose to the operators during transfemoral catheterization. We sought to investigate the impact on operator radiation exposure of various shielding drapes specifically designed for the radial approach. Background. Radial access for cardiac catheterization has increased due to improved patient comfort and decreased bleeding complications. There are concerns for increased radiation exposure to patients and operators. Methods. Radiation doses to a simulated operator were measured with a

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20

Kabbadj, S. "Monotone operator and the inexact entropic proximal point algorithm." International Journal of Mathematical Analysis 13, no. 6 (2019): 247–58. http://dx.doi.org/10.12988/ijma.2019.9427.

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21

Divband Soorati, Mohammad, Jediah Clark, Javad Ghofrani, Danesh Tarapore, and Sarvapali D. Ramchurn. "Designing a User-Centered Interaction Interface for Human–Swarm Teaming." Drones 5, no. 4 (2021): 131. http://dx.doi.org/10.3390/drones5040131.

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A key challenge in human–swarm interaction is to design a usable interface that allows the human operators to monitor and control a scalable swarm. In our study, we restrict the interactions to only one-to-one communications in local neighborhoods between UAV-UAV and operator-UAV. This type of proximal interactions will decrease the cognitive complexity of the human–swarm interaction to O(1). In this paper, a user study with 100 participants provides evidence that visualizing a swarm as a heat map is more effective in addressing usability and acceptance in human–swarm interaction. We designed

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22

Wattanawitoon, Kriengsak, and Poom Kumam. "Hybrid Proximal-Point Methods for Zeros of Maximal Monotone Operators, Variational Inequalities and Mixed Equilibrium Problems." International Journal of Mathematics and Mathematical Sciences 2011 (2011): 1–31. http://dx.doi.org/10.1155/2011/174796.

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We prove strong and weak convergence theorems of modified hybrid proximal-point algorithms for finding a common element of the zero point of a maximal monotone operator, the set of solutions of equilibrium problems, and the set of solution of the variational inequality operators of an inverse strongly monotone in a Banach space under different conditions. Moreover, applications to complementarity problems are given. Our results modify and improve the recently announced ones by Li and Song (2008) and many authors.

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23

Alfuraih, Abdulrahman M., Abdulaziz I. Alrashed, Saleh O. Almazyad, and Mohammed J. Alsaadi. "Abdominal aorta measurements by a handheld ultrasound device compared with a conventional cart-based ultrasound machine." Annals of Saudi Medicine 41, no. 6 (2021): 376–82. http://dx.doi.org/10.5144/0256-4947.2021.376.

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BACKGROUND: Ultraportable or pocket handheld ultrasound devices (HUD) may be useful for large-scale abdominal aortic aneurysm screening. However, the reproducibility of measurements has not been compared with conventional cart-based ultrasound machines. OBJECTIVES: Investigate the intra- and inter-operator reproducibility of a HUD compared with a conventional ultrasound machine for aortic screening. DESIGN: Analytical, cross-sectional. SETTING: Ultrasound department at a large tertiary care hospital in Riyadh. PATIENTS AND METHODS: Eligible male participants aged ≥60 years were invited to part

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24

Sudo, Shuta. "The Proximal Point Algorithm for Monotone Vector Fields on Complete Geodesic Spaces." Nonlinear Convex Analysis and Optimization: An International Journal on Numerical, Computation and Applications 4, no. 1 (2025): 1–15. https://doi.org/10.58715/ncao.2025.4.1.

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In this paper, we deal with monotone vector fields defined on geodesic spaces and their zero point approximation method. In an appropriate setting, we can define the resolvent operator for a given monotone vector field, and then that operator has many useful properties which are effective for the fixed point theory. We will show an approximation theorem for a monotone vector field with the canonical proximal point algorithm.

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25

Yu, Wei, Zonglin Li, Qinglin Liu, and Xin Sun. "OTPNet: ODE-inspired Tuning-free Proximal Network for Remote Sensing Image Fusion." Proceedings of the AAAI Conference on Artificial Intelligence 39, no. 9 (2025): 9671–79. https://doi.org/10.1609/aaai.v39i9.33048.

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Remote sensing image fusion aims to reconstruct a high spatial and spectral resolution image by integrating the spatial and spectral information from multiple remote sensing sensor data. Despite the remarkable progress of deep learning-based fusion methods, most existing methods rely on manual network architecture design and hyperparameter tuning, lacking sufficient interpretability and adaptability. To address this limitation, we propose a novel neural Ordinary Differential Equation (ODE)-inspired tuning-free proximal splitting algorithm, which splits remote sensing image fusion as two optimi

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26

Chen, Zan, Wenlong Guo, Yuanjing Feng, et al. "Deep-Learned Regularization and Proximal Operator for Image Compressive Sensing." IEEE Transactions on Image Processing 30 (2021): 7112–26. http://dx.doi.org/10.1109/tip.2021.3088611.

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27

HE, Bingsheng. "A new approximate proximal point algorithm for maximal monotone operator." Science in China Series A 46, no. 2 (2003): 200. http://dx.doi.org/10.1360/03ys9021.

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28

Mahey, Philippe, Said Oualibouch, and Pham Dinh Tao. "Proximal Decomposition on the Graph of a Maximal Monotone Operator." SIAM Journal on Optimization 5, no. 2 (1995): 454–66. http://dx.doi.org/10.1137/0805023.

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29

Akram, Mohd, J. W. Chen, and Mohd Dilshad. "Cayley approximation operator with an application to a system of set-valued Cayley type inclusions." Boletim da Sociedade Paranaense de Matemática 40 (February 7, 2022): 1–14. http://dx.doi.org/10.5269/bspm.51641.

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In this paper, we introduce and study a system of set-valued Cayley type inclusions involving Cayley operator and (H; )-monotone operator in real Banach spaces. We show that Cayley operator associated with the (H; )-monotone operator is Lipschitz type continuous. Using the proximal point operator technique, we have established a fixed point formulation for the system of set-valued Cayley type inclusions. Further, the existence and uniqueness of the approximate solution are proved. Moreover, we suggest an iterative algorithm for the system of set-valued Cayley type inclusions and discuss the st

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30

Khatibzadeh, Hadi, and Sajad Ranjbar. "Inexact Inertial Proximal Algorithm for Maximal Monotone Operators." Analele Universitatii "Ovidius" Constanta - Seria Matematica 23, no. 2 (2015): 133–46. http://dx.doi.org/10.1515/auom-2015-0031.

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Abstract In this paper, convergence of the sequence generated by the inexact form of the inertial proximal algorithm is studied. This algorithm which is obtained by the discretization of a nonlinear oscillator with damping dynamical system, has been introduced by Alvarez and Attouch (2001) and Jules and Maingé (2002) for the approximation of a zero of a maximal monotone operator. We establish weak and strong convergence results for the inexact inertial proximal algorithm with and without the summability assumption on errors, under different conditions on parameters. Our theorems extend the res

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31

Yin, Tzu-Chien. "Algorithmic and analytical approach to the proximal split feasibility problem and fixed point problem." Filomat 36, no. 2 (2022): 439–48. http://dx.doi.org/10.2298/fil2202439y.

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In this paper, we investigate the proximal split feasibility algorithm and fixed point problem in Hilbert spaces. We propose an iterative algorithm for finding a common element of the solution of the proximal split feasibility algorithm and fixed point of an L-Lipschitz pseudocontractive operator. We demonstrate that the considered algorithm converges strongly to a common point of the investigated problems under some mild conditions.

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32

Li, Zhenni, Shuxue Ding, and Yujie Li. "A Fast Algorithm for Learning Overcomplete Dictionary for Sparse Representation Based on Proximal Operators." Neural Computation 27, no. 9 (2015): 1951–82. http://dx.doi.org/10.1162/neco_a_00763.

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We present a fast, efficient algorithm for learning an overcomplete dictionary for sparse representation of signals. The whole problem is considered as a minimization of the approximation error function with a coherence penalty for the dictionary atoms and with the sparsity regularization of the coefficient matrix. Because the problem is nonconvex and nonsmooth, this minimization problem cannot be solved efficiently by an ordinary optimization method. We propose a decomposition scheme and an alternating optimization that can turn the problem into a set of minimizations of piecewise quadratic a

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33

Grammens, Jonas, Annemieke Van Haver, Imelda Lumban-Gaol, Femke Danckaers, Peter Verdonk, and Jan Sijbers. "Automated Landmark Annotation for Morphometric Analysis of Distal Femur and Proximal Tibia." Journal of Imaging 10, no. 4 (2024): 90. http://dx.doi.org/10.3390/jimaging10040090.

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Manual anatomical landmarking for morphometric knee bone characterization in orthopedics is highly time-consuming and shows high operator variability. Therefore, automation could be a substantial improvement for diagnostics and personalized treatments relying on landmark-based methods. Applications include implant sizing and planning, meniscal allograft sizing, and morphological risk factor assessment. For twenty MRI-based 3D bone and cartilage models, anatomical landmarks were manually applied by three experts, and morphometric measurements for 3D characterization of the distal femur and prox

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34

Wang, Shuang. "A Modified Regularization Method for the Proximal Point Algorithm." Journal of Applied Mathematics 2012 (2012): 1–14. http://dx.doi.org/10.1155/2012/567948.

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Under some weaker conditions, we prove the strong convergence of the sequence generated by a modified regularization method of finding a zero for a maximal monotone operator in a Hilbert space. In addition, an example is also given in order to illustrate the effectiveness of our generalizations. The results presented in this paper can be viewed as the improvement, supplement, and extension of the corresponding results.

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35

Wang, Yufeng, Hui Zhou, Shaohuan Zu, Weijian Mao, and Yangkang Chen. "Three-Operator Proximal Splitting Scheme for 3-D Seismic Data Reconstruction." IEEE Geoscience and Remote Sensing Letters 14, no. 10 (2017): 1830–34. http://dx.doi.org/10.1109/lgrs.2017.2737786.

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36

Vorontsova, E. A., A. V. Gasnikov, E. A. Gorbunov, and P. E. Dvurechenskii. "Accelerated Gradient-Free Optimization Methods with a Non-Euclidean Proximal Operator." Automation and Remote Control 80, no. 8 (2019): 1487–501. http://dx.doi.org/10.1134/s0005117919080095.

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37

Yang, Chengzhu, Yuantao Gu, Badong Chen, Hongbing Ma, and Hing Cheung So. "Learning Proximal Operator Methods for Nonconvex Sparse Recovery with Theoretical Guarantee." IEEE Transactions on Signal Processing 68 (2020): 5244–59. http://dx.doi.org/10.1109/tsp.2020.2978615.

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38

Kotagi, Vijeth J., Prabhu Kaliyammal Thiruvasagam, and C. Siva Ram Murthy. "Learn to Breathe: An Energy Efficient Inter-Operator Proximal Spectrum Sharing." IEEE Transactions on Green Communications and Networking 4, no. 3 (2020): 631–46. http://dx.doi.org/10.1109/tgcn.2020.2965183.

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39

Moudafi, A., and B. S. Thakur. "Solving proximal split feasibility problems without prior knowledge of operator norms." Optimization Letters 8, no. 7 (2013): 2099–110. http://dx.doi.org/10.1007/s11590-013-0708-4.

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40

Liu, Jingchang, Linli Xu, Junliang Guo, and Xin Sheng. "Adaptive Proximal Average Based Variance Reducing Stochastic Methods for Optimization with Composite Regularization." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 1552–59. http://dx.doi.org/10.1609/aaai.v33i01.33011552.

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We focus on empirical risk minimization with a composite regulariser, which has been widely applied in various machine learning tasks to introduce important structural information regarding the problem or data. In general, it is challenging to calculate the proximal operator with the composite regulariser. Recently, proximal average (PA) which involves a feasible proximal operator calculation is proposed to approximate composite regularisers. Augmented with the prevailing variance reducing (VR) stochastic methods (e.g. SVRG, SAGA), PA based algorithms would achieve a better performance. Howeve

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41

Garodia, Chanchal, Izhar Uddin, Bahaaeldin Abdalla, and Thabet Abdeljawad. "A modified proximal point algorithm in geodesic metric space." AIMS Mathematics 8, no. 2 (2023): 4304–20. http://dx.doi.org/10.3934/math.2023214.

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<abstract><p>Proximal point algorithm is one of the most popular technique to find either zero of monotone operator or minimizer of a lower semi-continuous function. In this paper, we propose a new modified proximal point algorithm for solving minimization problems and common fixed point problems in CAT(0) spaces. We prove $ \Delta $ and strong convergence of the proposed algorithm. Our results extend and improve the corresponding recent results in the literature.</p></abstract>

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42

Saleem, Naeem, Maneesha Tur Raazzia, Nawab Hussain, and Asim Asiri. "Geraghty–Pata–Suzuki-Type Proximal Contractions and Related Coincidence Best Proximity Point Results." Symmetry 15, no. 8 (2023): 1572. http://dx.doi.org/10.3390/sym15081572.

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The objective of this research paper is to establish the existence and uniqueness of the best proximity and coincidence with best proximity point results, specifically focusing on Geraghty–Pata–Suzuki-type proximal mappings. To achieve this, we introduce three types of mappings, all within the context of a complete metric space: an α−θ−Geraghty–Pata–Suzuki-type proximal contraction; an α−θ−generalized Geraghty–Pata–Suzuki-type proximal contraction; and an α−θ−modified Geraghty–Pata–Suzuki-type proximal contraction. These new results generalize, extend, and unify various results from the existi

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43

Jiang, Xin, and Lieven Vandenberghe. "Bregman primal–dual first-order method and application to sparse semidefinite programming." Computational Optimization and Applications 81, no. 1 (2021): 127–59. http://dx.doi.org/10.1007/s10589-021-00339-7.

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AbstractWe present a new variant of the Chambolle–Pock primal–dual algorithm with Bregman distances, analyze its convergence, and apply it to the centering problem in sparse semidefinite programming. The novelty in the method is a line search procedure for selecting suitable step sizes. The line search obviates the need for estimating the norm of the constraint matrix and the strong convexity constant of the Bregman kernel. As an application, we discuss the centering problem in large-scale semidefinite programming with sparse coefficient matrices. The logarithmic barrier function for the cone

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Gabeleh, Moosa, Elif Uyanık Ekici, and Manuel De La Sen. "Noncyclic contractions and relatively nonexpansive mappings in strictly convex fuzzy metric spaces." AIMS Mathematics 7, no. 11 (2022): 20230–46. http://dx.doi.org/10.3934/math.20221107.

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<abstract><p>A concept of fuzzy projection operator is introduced and use to investigate the non-emptiness of the fuzzy proximal pairs. We then consider the classes of noncyclic contractions and noncyclic relatively nonexpansive mappings and survey the existence of best proximity pairs for such mappings. In the case that the considered mapping is noncyclic relatively nonexpansive, we need a geometric notion of fuzzy proximal normal structure defined on a nonempty and convex pair in a convex fuzzy metric space. We also prove that every nonempty, compact and convex pair of subsets of

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Lee, Jeunghoon, Yongsung Park, Peter Gerstoft, and Kyungjun Lee. "Non-convex sparse beamformer." Journal of the Acoustical Society of America 157, no. 5 (2025): 3345–57. https://doi.org/10.1121/10.0036563.

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Sparse beamforming techniques, such as least absolute shrinkage and selection operator (LASSO) and fused least absolute shrinkage and selection operator (FL), underestimate source amplitude due to the soft-thresholding effect of the l1-norm regularization. For sparse beamforming, a new set of non-convex regularizers is introduced. They are designed to accurately recover source amplitudes—including those of extended sources—by reducing the shrinkage imposed on large coefficients. Integrating these non-convex penalties (NCP) within the FL framework, we propose the non-convex fused least absolute

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De Marchi, Alberto. "On a primal-dual Newton proximal method for convex quadratic programs." Computational Optimization and Applications 81, no. 2 (2022): 369–95. http://dx.doi.org/10.1007/s10589-021-00342-y.

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AbstractThis paper introduces QPDO, a primal-dual method for convex quadratic programs which builds upon and weaves together the proximal point algorithm and a damped semismooth Newton method. The outer proximal regularization yields a numerically stable method, and we interpret the proximal operator as the unconstrained minimization of the primal-dual proximal augmented Lagrangian function. This allows the inner Newton scheme to exploit sparse symmetric linear solvers and multi-rank factorization updates. Moreover, the linear systems are always solvable independently from the problem data and

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Deng, Kangkang, Zheng Peng, and Jianli Chen. "Sparse probabilistic Boolean network problems: A partial proximal-type operator splitting method." Journal of Industrial & Management Optimization 15, no. 4 (2019): 1881–96. http://dx.doi.org/10.3934/jimo.2018127.

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Zalev, Jason, and Michael C. Kolios. "Image Reconstruction Combined With Interference Removal Using a Mixed-Domain Proximal Operator." IEEE Signal Processing Letters 25, no. 12 (2018): 1840–44. http://dx.doi.org/10.1109/lsp.2018.2875348.

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Ahmad, Rais, та A. H. Siddiqi. "Mixed variational-like inclusions and Jη-proximal operator equations in Banach spaces". Journal of Mathematical Analysis and Applications 327, № 1 (2007): 515–24. http://dx.doi.org/10.1016/j.jmaa.2006.04.054.

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Liu, Xinmin, Charles Pelizzari, Andrew H. Belcher, Zachary Grelewicz, and Rodney D. Wiersma. "Use of proximal operator graph solver for radiation therapy inverse treatment planning." Medical Physics 44, no. 4 (2017): 1246–56. http://dx.doi.org/10.1002/mp.12165.

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